Mitt Romney rolled to a double-digit victory in Washington state's Republican presidential caucuses on Saturday night, his fourth campaign triumph in a row and a fresh show of strength in the runup to 10 Super Tuesday contests across America.

Rick Santorum and Ron Paul battled for second place, while Newt Gingrich ran a distant fourth.

Romney's victory came on the heels of twin primary triumphs over Santorum during the week in hard-fought Michigan and lightly contested Arizona, as well as a narrow win over Paul in Maine caucuses earlier in February.

Returns from caucuses in 60% of Washington state's precincts showed Romney with 37% of the vote, while Paul and Santorum each had 24%. Gingrich was drawing 11%.

Romney's win is worth at least 12 of the 40 delegates at stake. Paul and Santorum each won at least three. The rest remained unallocated, pending final returns.

Romney, Santorum and Gingrich were all campaigning in Ohio, the most intensely contested of the states holding nominating contests on Tuesday as the first caucus returns were reported from Washington state. Paul was in Washington state as the caucuses began, searching for his first victory of the campaign.

The Republican race has shared the political spotlight in the past few days with a controversy in which the conservative talkshow host Rush Limbaugh called a Georgetown University law student a "slut" and a "prostitute".

Limbaugh apologised on his website during the evening to the woman, Sandra Fluke, who had spoken out publicly in favour of a requirement for most insurance coverage to include contraception. Obama called Fluke on Friday to express his support. Polls show Obama's support among female voters on the rise since Republicans made contraception an issue.

The Republican presidential rivals have seemed reluctant to comment on Limbaugh's behaviour.

Washington's caucuses are the last before the Super Tuesday contests in 10 states that offer a total of 419 delegates to the party's national nominating convention. They stretch from Vermont to Alaska, but Ohio is the biggest and an important test for Romney, who has struggled to win over the conservatives who make up the party's base.

Santorum, a favourite of social conservatives, surged in national and state polls of Republican voters after winning contests in Minnesota, Colorado and Missouri. But he has fallen back under a barrage of negative TV ads from Romney and his supporters. His own lack of campaign organisation has raised questions about his ability to compete against the former Massachusetts governor over the long haul.

Santorum, campaigning across Ohio this weekend, emphasised social issues even while touting his plan to improve the nation's manufacturing base. In Cincinnati he called for fewer children born out of wedlock and fewer single-parent families. In Cincinnati he said there was less freedom in neighbourhoods "where there are no dads". And he suggested that the nation's inattention to conservative social values was "damning people".

Romney, befitting his frontrunner status, largely ignored his rivals while campaigning in Ohio to focus on Obama. He criticised the president after a woman attending a campaign rally in Beavercreek on Saturday said she had a daughter stationed in Afghanistan who believed the US mission there was unclear. The woman asked when Romney would bring the troops home.

"If your daughter is not familiar with the mission that she's on, how in the world can the commander in chief sleep at night, knowing that we have soldiers in harm's way that don't know exactly, precisely, what it is that they're doing there?" he said.

Romney said he would bring troops home "as soon as humanly possible as soon as that mission is complete".

Gingrich is staking his entire campaign on a big victory on Tuesday in Georgia, where the one-time speaker of the House of Representatives represented a suburban Atlanta district for 20 years.